PRX QUANTUM 2, 020343 (2021)

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Compact Ion-Trap Demonstrator

I. Pogorelov,1 T. Feldker,1 Ch. D. Marciniak ,1 L. Postler,1 G. Jacob,2 O. Krieglsteiner,2 V. Podlesnic,1 M. Meth,1 V. Negnevitsky,3 M. Stadler ,3 B. Höfer,4 C. Wächter,4 K. Lakhmanskiy,1,5 R. Blatt,1,6 P. Schindler,1 and T. Monz1,2,* 1 Institut für Experimentalphysik, 6020 Innsbruck, Austria 2 Alpine Quantum Technologies (AQT), 6020 Innsbruck, Austria 3 Institute for Quantum Electronics, ETH Zürich, 8093 Zürich, Switzerland 4 Fraunhofer-Institut für Angewandte Optik und Feinmechanik IOF, 07745 Jena, Germany 5 Russian Quantum Center, 121205 Moscow, Russia 6 Institute for and , 6020 Innsbruck, Austria

(Received 28 January 2021; revised 12 April 2021; accepted 7 May 2021; published 17 June 2021; corrected 30 June 2021)

Quantum information processing is steadily progressing from a purely academic discipline towards applications throughout science and industry. Transitioning from lab-based, proof-of-concept experiments to robust, integrated realizations of quantum information processing hardware is an important step in this process. However, the nature of traditional laboratory setups does not offer itself readily to scaling up system sizes or allow for applications outside of laboratory-grade environments. This transition requires overcoming challenges in engineering and integration without sacrificing the state-of-the-art performance of laboratory implementations. Here, we present a 19-inch rack quantum computing demonstrator based on 40Ca+ optical in a linear Paul trap to address many of these challenges. We outline the mechanical, optical, and electrical subsystems. Furthermore, we describe the automation and remote access compo- nents of the quantum computing stack. We conclude by describing characterization measurements relevant to quantum computing including site-resolved single- interactions, and entangling operations medi- ated by the Mølmer-Sørensen interaction delivered via two distinct addressing approaches. Using this setup, we produce maximally entangled Greenberger-Horne-Zeilinger states with up to 24 ions without the use of postselection or error mitigation techniques; on par with well-established conventional laboratory setups.

DOI: 10.1103/PRXQuantum.2.020343

I. INTRODUCTION architectures are trapped atomic ions, which have already met many requirements for fault-tolerant [13] quantum Quantum information processing as a computational computation [14–18]. paradigm has been proposed as an efficient means to With progressing capabilities among all platforms, the tackle computational challenges throughout science and attention has recently shifted away from proof-of-principle industry [1–6]. The rapid scaling of the computational implementations towards integration and scalability of potential with the number of quantum bits (qubits) is architectures [7,8,14,19–23]. The shift in development of the basis for widespread interest in realizing a quantum quantum computers from small-scale, expert-user devices information processor, or quantum computer. Tremendous to integrated, end-user-centric systems is analogous to progress has been made both experimentally and theo- the history of classical computation. It presents a host of retically in exploring and demonstrating hallmark capa- new challenges such as manufacturing many, effectively bilities of quantum information processors in numerous identical qubits, and improving the scaling in a num- architectures [7–12]. Among the most successful of these ber of control and readout lines, while maintaining low error rates [24–26]. The minimization of resource over- *[email protected] head incurred in quantum control techniques or is an ongoing challenge across architec- Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Fur- tures [14]. These challenges are prominent examples of ther distribution of this work must maintain attribution to the problems that need to be overcome as quantum devices author(s) and the published article’s title, journal citation, and scale to hundreds of qubits. It has become clear over the DOI. last decade that any device that can outperform classical

2691-3399/21/2(2)/020343(23) 020343-1 Published by the American Physical Society I. POGORELOV et al. PRX QUANTUM 2, 020343 (2021) high-performance computing for tasks relevant in indus- this setup into a fully self-contained, trapped-ion-based trial or applied science settings will require substantially quantum computing demonstrator. more qubits than current architectures can sustain [27–31]. In addition to a large number of qubits, such a device II. THE QUBIT SYSTEM should present the user with a hardware-agnostic interface, and require little to no maintenance by on-site person- The choice of atomic species in a trapped-ion exper- nel during standard operation. Meanwhile, all the basic iment is always based on trade-offs between beneficial routines should be automated and perform at the level suf- physical properties of a given species, and technical imple- ficient for fault-tolerance requirements. Finally, the device mentation challenges associated with it. Broadly speaking, should be deployable outside of well-controlled, low-noise atomic qubits can be either optical qubits, Zeeman qubits, laboratory conditions with purpose-built infrastructure. or hyperfine qubits. In optical qubits quantum informa- Demonstrating the capabilities of scalable architectures tion is encoded in two electronic states connected by an beyond laboratory implementations is therefore a crucial electric multipole transition with frequency in the optical next step. domain, and the excited state is long lived or metastable. In this work we present the first phase of our efforts In Zeeman or hyperfine qubits the information is encoded towards a compact, 50-qubit quantum computing demon- in magnetic sublevels of electronic ground states with tran- strator based on trapped ions as part of the AQTION sition frequencies in the microwave to radiowave domain. (Advanced Quantum computation with Trapped IONs) A species may host several different types of qubit dis- collaboration. It features a 1.7 × 1m2 footprint with high tinct in their implementation. Each species and qubit type mechanical stability, and scalable control electronics. We offers advantages and disadvantages that may benefit cer- describe the hardware concept and integration, and charac- tain applications more than others. At this stage no single terize the initial system performance including the entan- species or qubit type has been identified as ultimately supe- gling gate operation necessary for quantum computation. rior. The design goals and principles for our trapped-ion For a quantum computer to perform arbitrary compu- demonstrator are largely independent of the choice of ion tations, it is sufficient to implement arbitrary-pair, two- species or qubit type to reflect the flexibility that this fact qubit entangling gates in addition to single-qubit rotations requires. [32,33]. In a trapped-ion quantum computer these oper- In our particular demonstrator we use optical qubits ations are typically the result of interactions with laser encoded in the electronic state of the valence fields. Addressing individual qubits in a register with light in nuclear -free 40Ca+ ions. This choice is motivated beams is thus an essential component of universal quan- in part by technical considerations such as commercially tum computation efforts in trapped ions [34,35]. Meeting available semiconductor laser sources and high-quality the demands of state preparation and measurement [36– optics for all the required transitions. Transition wave- 38] in a scalable fashion is therefore a major challenge lengths are in the blue, red, and infrared parts of the optical in trapped-ion quantum computing. Consequently, the spectrum. Compared to transitions in the ultraviolet this demonstrator leverages industrial expertise to accomplish has several advantages such as reduced charging of trap scalable integration of light generation and delivery, in electrodes and substantially lower onset of solarization or particular single-site addressing essential for the trapped- photodarkening of optical components. Optical qubits can ion implementation. The demands of quantum control and be directly interacted with using only a single beam com- algorithmic compiling on the software stack with increas- pared to more complex beam geometries for Raman gates ing qubit and gate numbers are similarly challenging [39]. in Zeeman qubits or hyperfine qubits. A detailed description of the holistic software stack of Specifically, the qubit |1 state is the |4S1/2, mJ =−1/2 the AQTION platform, spanning device-specific control Zeeman state, which is coupled to the long-lived qubit |0 to hardware-agnostic end user algorithms, is beyond the state |3D5/2, mJ =−1/2. This excited state has a lifetime scope of the present paper and will be covered in upcoming of τ = 1.168 ± 0.007 s [40], and decays via an electric publications. quadrupole transition near 729 nm; see Fig. 1(a). This This manuscript is structured as follows. In Sec. II we transition has the lowest magnetic field sensitivity in the present an overview of the physical qubit implementation, manifold (5.6 MHz/mT) and is suitable for an effective as well as the means of control, preparation, readout, and two-level system as shown in Figs. 1(a) and 1(b). manipulation as necessary for computation. In Sec. III we The high magnetic field sensitivity compared to clock describe the main subsystems by functional groups, includ- transitions in hyperfine qubits can be mitigated by proper ing mechanical, optical, and electrical subsystems, as well magnetic shielding and stabilization [41]. A more funda- as automation features of the demonstrator. In Sec. IV mental limit of this optical qubit used is the lifetime of we turn to characterization measurements on the compos- the upper qubit state |3D5/2, mJ =−1/2. However, τ is ite system. This manuscript concludes in Sec. V, where about 4 orders of magnitude longer than typical 2-qubit we outline near-term hardware integration goals to expand operations (200 μs) and 5 orders of magnitude longer than

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(a) (b) axial trap direction, and 2N perpendicular to that in the mJ P radial trap directions [42]. 4 3/2 3D +5/2 P 5/2 4 1/2 866 nm 854 nm B. State preparation and readout Repump Quench 0 –1/2 State preparation proceeds in four steps. First, ions are –5/2 Doppler cooled at 397 nm and repumped near 866 nm. The D motional modes of the ion cloud or Coulomb crystal after Pumping 3 5/2 Sb cooling Qubit Doppler cooling will in general be in or close to the Lamb-

397 nm Dicke regime [43]. Second, polarization gradient cooling Doppler 3D 3/2 (PGC) is employed using two counterpropagating, orthog- 729 nm onally polarized beams blue detuned from the 4S1/2 ↔ Coherent 4S +1/2 4P / transition [44]. Polarization gradient cooling results 1/2 S 1 2 1 -1/2 4 1/2 in a thermal state of all motional modes of typically a few quanta of motion for common trapping parameters 40 + FIG. 1. Energy levels and relevant transitions in Ca for the much below the Doppler cooling limit [45]. Optical pump- quantum computing demonstrator. (a) Ground and excited state ing of the qubit manifold on the |3D / , m =−3/2→ fine structure manifold with electric quadrupole transitions for 5 2 J |4S / , m =+1/2 transition redistributes the electronic sideband (sb) cooling on the first red sideband, optical pumping, 1 2 J population from the initial mixed population of Zeeman and the mJ = 0 qubit transition. (b) Ground, excited and aux- + | =− / iliary levels in 40Ca with transitions for Doppler cooling and sublevels to the 4S1/2, mJ 1 2 state. The final step detection, repumping, and quenching of the excited state lifetime of preparation is sideband cooling on selected motional during sideband cooling. modes close to the ground state. The targeted modes in sideband cooling may consist of subsets of the N axial modes, or of the 2N radial modes closest to the selected single-qubit operations (15 μs). Thus, in the medium term, carrier transition that implements a gate operation. The gate fidelity is not limited by the fundamental physical cooling rate in sideband cooling is increased by quench- properties of the qubit but by the specifics of the technical ing the lifetime of the 3D5/2 manifold through coupling to implementation. the short lived 4P3/2 level via excitation at 854 nm. State- Preparation of the qubit system in our demonstrator selective readout is performed optically using fluorescence entails two tasks. First, loading of ions into the trap is measurements on the Doppler cooling transition, either site typically performed only when the qubit count has to resolved using a camera, or collectively (without spatial be changed. Second, preparation of the electronic and resolution) using an avalanche photodiode (APD). motional states of the ions that is performed before every experiment. C. State manipulation The universal gate set employed [46] in the demon- strator is spanned by arbitrary single-qubit operations and A. Ion loading the two-qubit entangling gate provided via the bichro- 40Ca+ is loaded into the trap either from a thermal source matic Mølmer-Sørensen (MS) gate [14,47]. Both single- or via ablation from a target. Either method produces and two-qubit gates are implemented using laser light ions with temperatures ranging from hundreds to thou- fields focused onto the ions. The effective Hamiltonian sands of kelvin. Atomic 40Ca features a low-lying excited governing (near) resonant single-qubit interactions in the state connected to the ground state via a dipole transition, demonstrator is given by [48] which enables isotope-selective, resonantly enhanced two- − ν ν −i[(ω−ω )t−ϕ] iη(ae i t+a†ei t) photon photoionization at commercially available laser H = σ+e eg e + H.c., wavelengths near 423 and 375 nm. The ionization pro- cess takes place at the center of the trap, where ions are where ω and ϕ denote the laser field frequency and phase, ν confined afterward by the trapping potential. The ions are is the motional mode frequency, ωeg is the qubit transition then Doppler cooled via an electric dipole cycling tran- frequency, and H.c. denotes the Hermitian conjugates. Fur- sition from 4S1/2 ↔ 4P1/2 at 397 nm. A repumping laser thermore,  denotes the Rabi frequency associated with near 866 nm prevents population trapping in the metastable the transition, η is the Lamb-Dicke parameter, a† is the 3D3/2 manifold. Doppler cooling alone may be sufficient phonon creation operator, and σ+ denotes the atomic (spin) to reach crystallization into a Coulomb crystal depending raising operator. This Hamiltonian assumes a well-isolated on the ion number and confining potential strength. Such two-level system for the interaction, uses the rotating wave Coulomb crystals of N ions support 3N bosonic motional approximation [43], and we neglect all other vibrational modes, N of which are parallel to the weakly confining modes. This Hamiltonian in the first-order Lamb-Dicke

020343-3 I. POGORELOV et al. PRX QUANTUM 2, 020343 (2021) approximation leads to a single-qubit unitary propagator III. TECHNICAL IMPLEMENTATION of the form Demonstrations of many of the requisite capabilities for ˆ (α) = −i(α/2)n·σ R e , quantum computation using trapped ions have been pre- where α is an angle that depends on the interaction strength sented using laboratory setups [14–18]. However, different and time, n is a unit vector, σ ={σx, σy , σz} is the Pauli design constraints apply when constructing traditional lab- spin vector, and n ·σ quantifies the strength of the inter- oratory setups or our modular approach. In the context of action along the three spin directions. In the atomic eigen- this work, we highlight the following. (i) The demonstrator basis this can be expressed in spherical-coordinate form, needs to minimize footprint while maintaining mechani- assuming that ω = ωeg, cal stability to move towards scalability without sacrificing performance. (ii) Implementing modularity with flexible − φ ˆ cos θ/2 −ie i sin θ/2 standard interconnects helps in reducing footprint and R(θ, φ) = φ , −iei sin θ/2cosθ/2 increasing rigidity, while also allowing replaceability and reconfiguration without major redesign, or manual realign- where θ and φ can be controlled via changing the ampli- ment. (iii) The demonstrator needs to be self-contained and tude or interaction time of the laser field, and its phase. rely as little as possible on purpose-built infrastructure. The propagator lends itself to the interpretation of rotating This puts restrictions on external supplies like power, cool- the state of a qubit on the Bloch sphere, and single-qubit ing, or environmental conditioning of the demonstrator operations are consequently referred to as single-qubit location. (iv) Scalability inevitably requires standardiza- rotations. tion. Utilizing established standards to leverage indus- Qubit-qubit interactions in linear ion chains forming trial processes and interfaces is therefore desirable. (v) along the weakly confining trap axis are mediated via Hardware-agnostic design and scalability require the use the bosonic bus of shared motional modes through spin- of automation, as well as remote operability. dependent optical dipole forces [49]. These forces are In this section we present our composite demonstra- generated via a bichromatic laser field detuned slightly tor’s setup whose overall concept is shown in Fig. 2. from the upper and lower sideband transitions of a selected The demonstrator setup is contained within two industry vibrational mode. The effective Hamiltonian governing standard 19-inch racks. Connections between the modules this interaction is given by inside each rack and between the two racks are achieved via electrical and optical patch cords, respectively. One of −i[(ωk−ωeg)t−ϕk] the two racks primarily houses modules related to gen- H = jkσj +e eration, switching, and routing of the required optical j =j ,j k=1,2 1 2 frequencies and is hence designated the optics rack.The η ( −iνt+ † iνt) × ei j ae a e + H.c., second houses the ion trap, associated infrastructure, and drive electronics, thus being designated the trap rack. where j enumerates ions and k enumerates the laser tones. Then, ωk and ϕk denote frequencies and phases of the ν bichromatic laser field, the closest motional mode fre- A. Mechanical assembly and environmental conditions quency, η the Lamb-Dicke parameter for this mode, ω j eg The primary mechanical assembly is composed of two the frequency of the qubit transition, and  the Rabi fre- jk industry standard 19-inch racks with a footprint of 0.85 × quencies of the kth beam for the j th ion. As before, a† is 1m2 each at a height of 2 m. Modules are largely free the phonon creation operator, σ + is the atomic (spin) rais- j of moving parts to improve mechanical rigidity, and long- ing operator. In the Lamb-Dicke approximation this leads term stability. Modules that require manual alignment are to a two-qubit unitary propagator of the form equipped with self-arresting slide drawers, such that main- −iχS2 tenance does not necessitate disassembly. The sole external UMS(χ) ≈ e x ⎛ ⎞ supply to the racks is one standard 16 A/230 V connector cos χ 00−i sin χ per rack, for a total power consumption of less than 3.7 kW ⎜ 0cosχ −i sin χ 0 ⎟ per rack. Temperature control inside the racks is provided = ⎝ ⎠ , 0 −i sin χ cos χ 0 by forced-air cooling and passive cooling fins throughout −i sin χ 0 0 cos χ the modules. Air flow is restricted across free-space opti- cal parts by appropriate enclosures. This prevents beam where χ can be controlled with laser field power or inter- pointing instability and phase fluctuations induced by the = σ action time and Sx j j ,x is the total spin along x.The moving air column. The racks are closed with doors in bichromatic beam parameters should obey certain relations standard operation, improving directionality of air flow to guarantee that the motional state is disentangled from for better cooling, and protecting the equipment from the ions’ spin states at the end of the interaction [50,51]. dust.

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FIG. 2. Simplified scale model of the quantum computing demonstrator housed in two 19-inch racks with major components labeled. Modules in red correspond to optical systems, green for communication and readout, blue electronics and amplifiers, yellow fiber routing and switching, and purple for miscellaneous core modules. The “optics rack” contains primarily light generation, switching and routing modules with associated electronics. It additionally houses the coherent radio frequency (rf) and digital signal generation module. The “trap rack” houses the main trap module with associated drive electronics, as well as the communications and remote control hub. Interconnects between modules and racks via electrical and optical patch cords. Semitransparent red is the planned 729 nm light generation module.

1. Ion trap and vacuum apparatus The Paul trap itself is located inside a compact stainless The 40Ca+ ions are confined in a linear Paul trap (AQT steel spherical octagon vacuum chamber. Six diametrically Pine trap) consisting of electrodes machined from gold- opposing, nonmagnetic fused silica DN40 viewports with plated titanium, and an alumina holder that serves as an antireflective coating allow for low numerical aperture ≈ mounting and electrical isolation between the electrodes. (NA) optical access on the trap perimeter with NA 0.05. The macroscopic trap design of the demonstrator consists Additionally, a viewport with a clear aperture of 44.2 mm of four blade electrodes and two endcaps, and is a variant in the trap mounting flange provides optical access with a ≈ of earlier designs employed previously in the Innsbruck medium NA 0.29 for imaging of ions to an avalanche ion trapping group [52,53]. The distance from the cen- photodiode. From the opposing side of the vacuum cham- ter of the trap to the surface of the blade electrodes is ber, a reentrance viewport with clear aperture of 71.2 mm r = 0.57 mm, while the endcap-endcap distance is z = at a distance of 18.3 mm to the trap center provides opti- 0 0 = 4.5 mm. cal access via a NA 0.6 objective lens (Photon Gear, Radio frequency voltage is applied to two opposing 18WD Atom Imager Objective) for resolved ion imaging blade electrodes, and a positive static (dc) voltage to the and illumination. endcaps. A set of additional electrodes allows for com- The trap mounting flange is equipped with feedthroughs pensation of stray electric fields in order to reduce excess for electrical connection to the trap electrodes, calcium micromotion. The remaining two blade electrodes are held oven, and the PT100 temperature sensor. Two nonevap- at a dc potential, but may be supplied with an out-of-phase orative getter pumps (SAES NexTorr Z200) provide the rf potential for symmetric drive, if desired for complete main pumping capacity to the chamber. A small ion getter cancelation of axial micromotion. The trap features a ther- pump (SAES CapaciTorr Z100) additionally pumps noble mal calcium source (oven) for photoionization, as well gases and provides pressure monitoring. Material selec- as an ablation target. An in vacuo PT100 temperature tion for chamber construction is again restricted to low sensor allows for temperature monitoring of the trap in magnetic permeability, with the exception of permanent operation. magnets required for pump operation. The trap assembly uses exclusively nonmagnetic mate- Permanent magnets are further used in Halbach and rials, specifically titanium, copper, alumina, and austenitic Helmholtz configurations to provide the quantization field stainless steel (grade 1.4429 or equivalent) to minimize for the qubits. These are mounted directly to the vac- distortion of the magnetic environment. uum chamber. The resulting homogeneous field in the

020343-5 I. POGORELOV et al. PRX QUANTUM 2, 020343 (2021) trap center has an angle of 66◦ and 34◦ to the trap axis supports. The supports in turn connect to sliding rails on and the imaging axis, respectively. The magnitude of ball bearings through active vibration damping elements the total field produced is B0 = 0.50 mT. Temperature- (Accurion Vario) based on preloaded springs and magnetic compensated samarium cobalt magnets are employed to repulsion elements. Measurements of the isolators’ mag- reduce magnetic field fluctuations to a minimum. Their rel- netic fields show that their influence at the ions’ position is ative change in magnetic field strength with temperature is below the ambient magnetic field level. The sliding drawer −5 −1 δTB ≈ 1 × 10 K . Furthermore, three sets of compen- allows for easy access during installation and maintenance sation coils along three orthogonal axes allow for control by clearing the main rack structure. The majority of the and stabilization of the magnetic field at the ion location in drawer footprint is enclosed in a μ-metal (ASTM A753 both absolute value and gradient. Alloy 4) shield (supplied by Magnetic Shield Ltd.) for magnetic isolation, which has a limited number of penetra- tions for electrical and optical access. Active instruments 2. Trap support infrastructure and environmental and electronics that can cause magnetic field noise are isolation outside the shielded section wherever feasible. The Paul trap and accompanying vacuum chamber are the most critical components with respect to environmen- tal disturbances like thermal, mechanical, or magnetic field fluctuations. The employed 40Ca+ implementation main- B. Optical subsystems tains sensitivity to magnetic field noise that can limit Interaction with and readout of the qubits is primarily attainable coherence times. Qubit operations depend on undertaken using optical fields in the presented demonstra- the amplitude, phase, and frequency of the interacting tor. The ability to manipulate and read out single qubits light fields. Therefore, any fluctuations on those quanti- with light is thus central to its operation. Optical and ties, as for example caused by beam pointing instabilities, optoelectronic subsystems consequently occupy an appre- will adversely affect operation fidelity. Consequently, these ciable portion of the available space and complexity. In the critical components are situated in an environmentally iso- following we discuss the generation and stabilization of lated housing, as shown in Fig. 3, which we refer to as the the requisite lasers, present the light routing and address- trap drawer. The drawer itself, designed at AQT, makes up ing capabilities, and finally summarize the readout and the bottom layer of the trap rack, and is fastened to it via detection components.

FIG. 3. Schematic of the trap drawer detail, focusing on the trap proper and mechanical components, displayed with extended (opened) drawer. Three sets of compensation coils each with a Helmholtz and anti-Helmholtz coil per holder (red) together with four sets of permanent magnets in Helmholtz (blue, left leader) and Halbach (blue, right leader) configurations define and compensate the magnetic environment. A μ-metal shielding encloses the trap setup except for penetrations allowing electrical and optical access. Active vibration isolation and thick honeycomb-lattice breadboards provide mechanical stability. A fan outside the shielding provides cooling for components close to the shield.

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1. Laser light generation and stabilization (MSquared SolsTiS) locked to a high-finesse optical cav- ± The demonstrator is equipped with three principal laser ity, resulting in a linewidth of 3.6 0.4 Hz [38]. The seed generation modules, as indicated in Fig. 4.First,aQ- light is fed into the TA via an optical fiber with active fiber switched (pulsed) laser (Coherent Flare NX) situated out- noise cancelation [55]. The TA has an output power of 500 side the magnetic shielding in the trap drawer emitting mW at a seed level of 15 to 30 mW, which is sufficient at 515 nm provides highly energetic pulses for ablation to drive the amplifier gain into saturation. The bichro- loading [54]of40Ca+ from the in vacuo target. Second, a matic light fields required for the Mølmer-Sørensen inter- multicolor diode laser (MDL) generation module (Toptica, action are generated by supplying a two-tone rf signal to MDL pro) provides light for all incoherently driven inter- the acousto-optic modulator (AOM) further downstream. actions: Doppler and polarization gradient cooling at 397 Future hardware upgrades will be composed of a compact, nm, line broadening (“lifetime quenching” for the qubit diode-based laser system stabilized to a high-finesse cav- reset) at 854 nm, repumping at 866 nm, and 423 nm light ity, which is completely contained in the rack. The pending used in the first (resonantly enhanced, isotope-selective) system upgrade features a specified linewidth of less than step for photoionization. This MDL setup is supplemented 2 Hz and an output power of greater than 200 mW after by a free-running laser diode (Toptica iBeam smart) pro- fiber noise cancelation. viding light at 375 nm for the second (nonresonant) pho- Both ablation loading and photoionization inherently toionization step to the continuum. The last major light have no need for stringent frequency stabilization. On the 40 + generation module provides light at 729 nm for sideband other hand, all interactions with Ca require precise con- cooling, optical pumping, and the coherent qubit control trol of the absolute frequency of the respective lasers to transition. Preliminary operation of this module uses a maintain efficient operation. The MDL unit has therefore tapered amplifier (Toptica, TA pro), which is fed by seed been extended to provide two fiber-coupled feedback out- light generated outside of the rack until the integrated puts combining all four frequencies on two patch cords, laser source is installed. The seed light is derived from which are fed to a dedicated stabilization module. The sta- an ultrastable titanium sapphire (Ti:Sa) master oscillator bilization unit should provide reliable low-noise frequency locking along with low long-term drift rates. In addition to these general requirements we need to comply with the Stabilization module demonstrator’s design principles, which demand compact- ness, remote control access, and automation features. The AQT Beech Trap module module used here to comply with these requirements is the AQT Beech module. Inside, all lasers are locked to a ref- Toptica MDL pro 515 erence cavity. The cavity in turn is stabilized via a transfer lock to an atomic transition in a gas cell. The details of this 397 system will be presented in a separate publication. 375 423

Fiber distribution 854 module 2. Light delivery, switching, and addressing 866 The delivery subsystem handles the necessary routing To light routing and spatial distribution of the light colors throughout the setup. This includes collective delivery for all the lasers as well as site-selective (addressing) delivery for coherent qubit control. The system provides control over the tem- poral and intensity profile of the light fields via amplitude Toptica TA pro From Ti:Sa FNC 729 shaping, amplitude stabilization, and amplitude switching. The optical subsystems have been made modular when- 729 module ever possible to provide replaceability and readjustment without disturbing other parts of the setup. Intermod- FIG. 4. Schematic of the principal light generation modules. ule connection is achieved via fiber-optical patch cords A modified Toptica MDL pro unit produces four of the five laser in line with the requirements on stability and modular- colors needed for incoherently driven excitations. Their output is fiber coupled to a frequency stabilization module. A free-running ity. Polarization-maintaining single-mode optical fibers are laser diode is additionally installed downstream to provide the used for delivery throughout due to the polarization sen- final incoherent excitation color. Laser colors within the qubit sitivity of optical transitions between Zeeman sublevels manifold are generated by a Toptica TA pro seeded by light from in the magnetic field. Typically, free-space optics outper- an ultrastable MSquared SolsTiS Ti:Sa master oscillator present form fiber optics in terms of transmission loss and polar- in the laboratory. ization extinction ratio. This gap in performance grows

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Switching PGC 2 from below. The four fiber access ports are each equipped module Fiber distribution with a fast and slow photodiode for monitoring power and module stabilization close to the ion position. Double-pass AOMs PGC 1 Individual control over the amplitude of not only each From li Doppler 397 color, but each laser beam, is required by nature of the gate-based interaction. Amplitude shaping is implemented g 423 PDs ht via free-space double-pass AOMs. These shaping AOMs g

eneration 854 375 further provide the individual frequency offsets required 866 To wavemeter to bridge the detuning between the frequency stabiliza- 729 tion cavity resonance and required transition frequency.

Double-pass Addressed They are situated inside dedicated rack units as part of FNC AOMs the switching module. An additional mechanical shutter Switching module Global is inserted in the Doppler cooling beam path, normally 729 blocking the undiffracted zeroth order after the switching Fiber AOMs AOM. Opening the shutter gives access to a laser that is red detuned by approximately 300 MHz from the main cycling Single-ion transition, and can be used to refreeze a molten ion crystal. 515 addressing The light switching modules are followed by a dedicated Trap fiber distribution module, where free-space optics are used module to overlap and fiber-couple beams into patch cords for final delivery. The fiber distribution and switching mod- ules further incorporate photodiodes for continuous power monitoring on all colors throughout the beamline. FIG. 5. Schematic of light delivery, switching, and addressing modules. Light is fiber delivered to dedicated switching modules The beamline for the qubit manipulation laser is built utilizing free-space double-pass AOMs, after which overlap- analogously, with the addition of active fiber noise can- ping and fiber routing to their final destination is handled on celation, preceding the switching module. The qubit laser a fiber distribution module for incoherent interactions. Photodi- is split on the switching board into two beams before odes (PDs) are placed throughout the beamline for continuous passing a respective free-space double-pass AOM. The power monitoring. The qubit laser system has similar switching first goes directly into a FAOM and is sent to the trap and routing capabilities, with the addition of fiber noise cancela- along its symmetry axis for collective operations on all tion (FNC), and fiber AOMs for improved the on-off extinction qubits simultaneously. The second is used for single-ion ratio, bichromatic modulation for Mølmer-Sørensen interactions, addressing. Light from an addressing unit is delivered to and light field parameter control. One of two approaches is used to deliver addressed light; see Figs. 6 and 8. the ions via free space. For the addressing units, we trial two different approaches. The first uses a fixed number of fiber-coupled rigid waveguide channels with micro-optics for shorter wavelengths. Consequently, intermediate free- that are imaged onto the ion. The second is based on two space optics are employed where fiber-based components crossed acousto-optic deflectors (AODs) for positioning of perform insufficiently. Figure 5 shows a schematic of the the addressed beam [56]. An overview of these approaches delivery subsystem. is shown in Fig. 6. The arrangement of light fields arriving Four main delivery points for optical access are arranged at the ion location is shown in Figs. 7 and 8. orthogonal to the high-NA access ports of the vacuum For the micro-optics approach, light is sent to an addi- chamber. Each of these is equipped with a fiber collimator tional splitting module with a fixed number of output for delivery. The collective qubit laser at 729 nm following channels, followed by individual FAOMs for light switch- the fiber-coupled AOM (FAOM) propagates through holes ing before being fed to the unit. The FAOMs have a in the trap endcaps. On the opposing side is another single- center frequency of 150 MHz, an on/off extinction ratio mode fiber with the two photoionization colors. Delivery of approximately 40 dB, and imprint the bichromatic side- of all other collective beams happens at 45◦ to the trap axis. bands onto the laser, as required for Mølmer-Sørensen A large-mode-area photonic crystal fiber (NKT Photonics interactions. The presence of an individual FAOM per ion LMA-PM-5) delivers the superimposed Doppler cooling has the further benefit of allowing individual control of laser, refreeze laser, one of the two PGC lasers at 397 nm, the light field’s parameters for each channel, to, e.g., inter- as well as the repumping and quench lasers at 866 and act with different motional modes for efficient coupling, to 854 nm, respectively. A single-mode fiber on the opposing adjust each ion’s Rabi rate, or to compensate for potential port delivers the remaining second PGC laser to com- individual qubit frequency shifts. At the stage presented plete the scheme. The high energy 515 nm light pulses here, the splitting board is composed of a diffractive optic for ablation loading are coupled free space into the trap splitting the input light eightfold. The output fibers of the

020343-8 COMPACT ION-TRAP QUANTUM... PRX QUANTUM 2, 020343 (2021)

(a) grows quadratically with the number of rf tones applied. Consequently, the power available per beam decreases quadratically with the number of tones as well.

3. Imaging optics Optical readout can be performed in two ways. First, spatially resolved imaging of the ion string using an elec- tron multiplying charge-coupled device camera through use of a near-diffraction-limited, high-NA objective. Second, not spatially discriminating (collective) light detection through a single-photon-counting avalanche pho- todiode and medium-NA optics. Both detection paths are situated orthogonally to the trap axis and the plane that (b) contains all laser beams to minimize stray light onto the detectors. Additionally, this arrangement gives the largest possible numerical apertures through the vacuum chamber view ports for large collection efficiencies on the imaging systems. Both the APD and camera are placed outside of the magnetic shielding, where light exits through penetra- tions in the shield. Such an arrangement helps to minimize the amount of stray magnetic fields close to the trap cham- ber that may be caused by the readout electronics in the detectors. Readout through the APD serves as a means of detec- tion in trap characterization and system diagnostics, but is only suitable for small system sizes, and does not offer FIG. 6. Simplified illustration of the addressing approaches site selectivity. The imaging system employed for APD trialed, dimensions not to scale. (a) A fiber-coupled rigid waveg- ≈ uide with micro-optics delivers light via a shrinking telescope to readout has a medium numerical aperture of NA 0.29, × the main objective and onto the ions. Beam separations are fixed. with a magnification of about 1, and a field of view of (b) A pair of crossed AODs with a relay telescope delivers light about 60 μm. A single ion driven far into saturation on the to the main objective and onto the ions. Beam separations are cycling transition with these parameters yields a photon variable. flux of order 500 kcts/s on the APD given the NA, optical losses, and device quantum efficiency. The primary imaging system features a high numeri- FAOMs are coupled into a waveguide and imaged onto cal aperture of NA ≈ 0.5 limited by the trap apertures. the ion crystal via the main objective lens described in This system is used both for site-selective readout and Sec. III B 3. This addressing unit is provided by Fraun- manipulation of individual ions (single-site addressing). hofer IOF. The details of this unit are beyond the scope The system’s main objective is a compound lens designed of this paper and will be summarized in a forthcoming to operate near the diffraction limit for the detection light publication. at 397 nm as well as for the addressing light at 729 In the AOD approach on the other hand light is deliv- nm. A dichroic mirror is used to overlap the two colors ered via a single fiber. The two AODs are oriented at an through this main objective, while compensation optics in angle of ±45◦ with respect to the ion string symmetry the imaging path correct for abberations introduced by the axis. Beam steering without incurring position-dependent dichroic mirror. Imaging design targets are a magnifica- frequency shifts is achieved by utilizing crossed pairs of tion of approximately ×29 at a field of view of 150 μm AODs where the frequency up-shift from one unit (using to match the detector size. The design modulation transfer the +1st diffraction order) is exactly canceled by the sec- function exceeds 0.5 at a resolution of 0.5 μm over the full ond (using the −1st diffraction order). Angular deflection field of view, well in excess of what is required to resolve through the AODs is converted to translation in the ion single ions with a typical spacing of d0 ≥ 3 μm. plane by action of the main imaging objective. Driving The main objective’s mounting provides five degrees the AODs with multiple rf tones allows for simultane- of freedom for precisely aligning the optical axis with ous addressing of multiple ions at the cost of additional the ions necessary to achieving these tight specifi- beams situated above and below the ion string. These cations. First, translation perpendicular to the optical beams have a nonzero frequency shift, and their number axis (X -Y translation) is achieved via flexure joints in

020343-9 I. POGORELOV et al. PRX QUANTUM 2, 020343 (2021)

FIG. 7. Schematic of the trap drawer detail, focusing on optical and detection components, displayed with extended (opened) drawer. Optical interfacing with the ions is achieved via fiber delivery for Doppler cooling, polarization gradient cooling, quenching and repumping (red pair), as well as the collective qubit laser (blue, left) and photoionization (blue, right). Free-space delivery of the pulsed ablation laser is achieved via access from below (green). Single-site addressing lasers are steered by an addressing unit, and overlapped with the resolved detection path (high-NA objective, yellow) on a dichroic beam combiner (silver). Compensation optics for resolved light counter abberations introduced via the combiner. Collective imaging to an APD leaves at the back of the chamber (purple). Detection electronics and light sources are situated outside the μ-metal shielding. Fiber AOMs allow pulsing and imprinting of bichromatic sidebands onto the qubit lasers. the objective’s mounting plate, which are actuated via switches that connect individual devices to the control fine-pitch micrometers. Second, pitch and yaw can be computer. adjusted using fine-pitch screws with a spring-loaded kine- The electronic outfitting of the demonstrator setup is matic three-point mounting. Piezoelectric actuators allow based largely upon modular components. The demonstra- for fine tuning the position on all three adjusters in addi- tor is controlled and driven by both analog and digital tion to coarse alignment via thumbscrews. The final degree electronics. The trap blades providing radial confinement of freedom is translation along the optical axis (Z trans- are driven by a dedicated rf signal generator (Rhode & lation or focusing). Coarse alignment is achieved via the Schwarz SMB100B) that is amplified via a helical res- fine-pitch threading used to secure the objective lens. This onator [57]. The ion’s secular frequency is actively sta- thread is guided through a tight-fitting tube that affords bilized by a feedback circuit actuating on the supplied high repeatability. Fine adjustment is achieved by using trap rf [58]. In addition, the demonstrator makes use of the kinematic mount’s three piezoelectric transducers in state-of-the-art phase-coherent digital signal generation, tandem for pure translation. Realignment and refocusing real-time control, and in-sequence decision making based using manual thumb screws is typically only necessary on field programmable gate arrays (FPGAs) to perform after making major changes to the system. Fine adjustment digital (pulsed) operations. of the addressing using the piezo actuators is typically done once a day or after opening of the trap drawer. 1. Experimental control electronics The laser pulses used for manipulating the states of the ions are controlled using acousto-optic modulators. These C. Electronics, control, and automation require radio frequency signals that are precisely timed Access to and control of the experimental platform and phase coherent (interpulse, interchannel, and inter- is managed by a rack-mounted desktop computer that module). For typical rf pulses several microseconds in is accessed via Ethernet. Both racks feature Ethernet length, the timing resolution needs to be less than 10 ns

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digital signals are manipulated using a FPGA-based modu-

854 lar experimental control system developed at ETH Zurich, Doppler B 866 known as “Modular Advanced Control of Trapped IONs” (M-ACTION) [59]. It uses a “star” topology as shown in PGC 1 Fig. 9, with a central master control board that communi- 729 375 cates with the control PC via a custom Ethernet protocol, and multiple peripheral boards providing rf output [60]. Global 423

Side view The peripheral boards communicate with the master via a low-level low-voltage differential-signaling-based pro- tocol through a backplane into which all the boards are 515 inserted. PGC 2 The master board is a commercially available Avnet Zedboard extended with custom boards for digital I/O and B APD board-to-board communication. It is centered around a Xil- inx Zynq system on chip, which holds both a FPGA core used for low-level deterministic signal handling, and a dual 729 375 core 667 MHz ARM A9 CPU suitable for higher-level con- Global 423 trol and real-time computations. These include Boolean Top view Top decisions such as those in quantum error correction, as Camera 729 well as more sophisticated Bayesian decisions featuring Addressed feedback of a continuous parameter to the experimental hardware [59,61]. The FPGA core, on the other hand, mon- itors the peripheral rf boards, and controls the digital I/O FIG. 8. Geometric arrangement of beam delivery; beam polar- ization indicated where required. The Doppler cooling beam, the that requires precise timing. repumping and quenching beams, as well as PGC beams enter The rf peripheral boards each consist of four direct- the chamber at 45◦ to the trap axis. The collective 729 nm beam digital synthesis (DDS) chips (Analog Devices AD9910), is delivered through a hole in the trap endcap. Photoionization controlled by a standalone FPGA (Xilinx Spartan-6 beams enter through a hole in the opposing endcap. The medium- XC6S150T) with sufficient memory and a pulse sequence NA port is used for collective readout of the whole ion chain processor to independently execute most typical exper- with an APD. The high-NA access port is used for single-ion iments without intervention from the master [60]. In addressing and readout with a camera. situations where intervention from the master board is required, such as when real-time feedback is being car- ried out, the latency between an input to the master and a change in pulse sequence on the peripheral cards is around to control pulse lengths to better than 1%, and the tim- 5 μs. Recent revisions of the rf board also feature two ing jitter must be below a few hundred picoseconds to analog-to-digital converters, and support on-board servo ensure repeatability. Digital input/outputs (I/Os) with sim- regulators for intensity stabilization with sample and hold ilar timing resolution and jitter are also required, both for synchronous to the local pulse sequences. Proportional- triggering external devices such as rf switches, shutters, or integral-differential (PID) regulator gains and setpoints arbitrary waveform generators, and for counting photon- may be altered in sequence to help cope with external arrival pulses from photomultipliers or APDs. These rf and nonlinearities.

Control PC FIG. 9. M-ACTION exper- Ethernet imental control system. The master board acts as the hub of the system, synchronously rf peripheral boards running experimental sequences Master Zedboard involving the digital I/O and rf outputs the rf peripheral boards, and Digital outputs managing communications with 32 32 the control PC. PID lock statuses 8 Photon counters 8 8 Analog inputs Backplane links (rf stabilization)

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The aforementioned rf boards support a single-tone out- given angle to hardware instructions such as laser pulses put per channel, requiring multiple channels to be added with a certain power and duration. It is expected that this together for multitone quantum gates. Additionally, the feature, in combination with remote access to the setup, complexity of a pulse is limited by the bandwidth of the will greatly improve the ease of use for collaborators. interface between the FPGA and the DDS chips. A new rf generation board using 1 GSa/s DACs controlled directly IV. SYSTEM CHARACTERIZATION by a more powerful FPGA, as well as 32 GB of local memory, is currently being developed to overcome these We now turn to characterizing the demonstrator setup. bottlenecks. A suite of common measures and experiments is used to In-sequence decision making is performed based on evaluate the engineering approaches for the rack-based predetermined conditional decisions or “branches”. This architecture. The section begins with outlining standard predetermination allows FPGA memory management. operation parameters for the ion trap. Measurements on the Branches are subsequences that are executed if in- mechanical stability of the rack and the performance of the sequence detection fulfils the branch conditions. Photon active vibration isolation system are presented. We show count data from either a camera or APD are used directly measurements on imaging system performance, as well on the FPGA to determine whether a branch condition is as addressing capabilities using two different addressing met. unit devices. We finally turn to measurements pertain- A simple example would be of a state transfer |S→|D ing to the operation of the demonstrator itself, such as by means of a π/2 pulse. If at the decision making point characterization and compensation of the magnetic field |S is measured, that is, many photons are scattered in gradients, coherence times, ion temperature and heating the detection window, then the FPGA determines that the rates, and gate performance for single- and pairwise-qubit condition for state transfer to |D is met, and executes a interaction. π-pulse to transfer the population into |D. If, on the other hand, |D is detected, that is, few photons are scattered, A. Trapping parameters then this additional pulse is not executed. A more compli- The Paul trap’s radial confinement voltage is supplied to cated example is given in the literature [62], which uses a helical resonator, in order to filter and impedance match the same hardware in a separate experiment. the rf drive to the trap [57] that results in a voltage step up at the trap side. The loaded resonator oscillates at a drive frequency of rf ≈ 2π × 27.4 MHz. It is driven with an 2. Experimental control software input power of up to Pin,max = 10 W. The trap endcaps The experiment hardware is operated using two lay- are supplied with a voltage of up to Vec ≈ 1000 V. An ion ers of control software. The lower layer, running on the trapped in the trap will oscillate at the resulting pseudopo- master board, is written in C ++ and provides access tential’s three fundamental trap frequencies ωax,andωrad to the functionality of M-ACTION to a PYTHON-based that can be measured by external excitation with oscillating higher layer running on the control PC. This higher layer is fields (“tickling”) [65] or by sideband spectroscopy [66]. used for day-to-day experimental operation and program- These trap frequencies are (nearly) identical to the center- ming, while the lower layer can be used to implement of-mass motional excitations of ion clouds or crystals in high-performance real-time computations, or extend the the three trap directions. We determine the secular frequen- 40 + capabilities of M-ACTION. cies for a single Ca of ωrad ≈ 2π × 3 MHz in the radial A graphical user interface (UI) gives direct feedback to direction with 10 W input power, and ωax ≈ 2π × 1MHz the operator, and is used for the majority of day-to-day along the trap axis at about 1000 V endcap voltage. In experimental control tasks. Script-based implementations situ temperature measurements using a PT100 thermis- of pulse sequences allow for versatile extensions to low- tor give a temperature of the trap that depends on the rf ◦ level pulse patterns available from the UI. Automated rou- drive power. The temperature reaches about Tmax ≈ 100 C tines for calibration, maintenance, and error handling, such after sustained operation at Pin,max = 10 W. The pres- as Rabi frequency tracking, frequency drift compensa- sure in the vacuum chamber as measured by the pump’s tion, and string recrystallization, are supported to maintain gauge is 1.5 × 10−11 mbar. The pressure reading does not the system at high fidelity without constant supervision. depend on the drive power, indicating little outgassing Quantum circuits are executed via a high-level language from adsorbed contaminants on the trap surfaces. made in house, called PySeq, which acts as an intermedi- The ion gauge’s pressure measurement is performed at ary between state-of-the-art frameworks like Cirq [63]and the pump location instead of the ion location. Differen- [64] and close-to-hardware descriptions on the laser tial pressures in ultralow vacuum conditions can thus lead pulse level. PySeq is, similar to Qiskit, a PYTHON pack- to an underestimation of the pressure at the ion location. age and provides a convenient abstraction layer translating Consequently, we independently determine the pressure at objects like rotations around an axis for a the ion location via collision rate measurements [67,68].

020343-12 COMPACT ION-TRAP QUANTUM... PRX QUANTUM 2, 020343 (2021)

Collisions with residual thermal atoms melt the ion crystal (a) and thus limit the stability of ion crystals in the trap. We distinguish between two different types of collision event: those that melt the crystal and cause ions to change sites in the refrozen crystal, and those that lead to molecule for- mation via chemical reactions that changes the number of (bright) ions. Detection of reconfiguration events is done by observing the position of nonfluorescing, cotrapped ions (defect hopping). We measure a collision rate of −1 col = 0.0025 ± 0.0011 s per ion by observing recon- figuration events in a three-ion crystal consisting of two (b) bright 40Ca+ and one dark, cotrapped ion, which corre- −11 sponds to a pressure of pion = (9.7 ± 4.2) × 10 mbar assuming collisions with H2 [68]. This means that even a 50-ion chain is unlikely to experience a collision during the qubit coherence time of 100 ms. Ion loss may occur when collisions are sufficiently strong to lead to unstable ion trajectories, or when chemical reactions cause forma- tion of dark ions. By observing an ion crystal of 32 bright 40Ca+ ions over the course of 12 h we observe the loss of only one ion from the trap. FIG. 10. Displacement (amplitude) spectral densities (ASDs) (a) parallel to the floor (horizontal) and (b) perpendicular to the floor (vertical) calculated from time series data obtained with B. Mechanical stability and active damping piezoelectric shear accelerometers. Traces show equivalent dis- Mechanical instability affects quantum computing placement spectral densities of the electronic noise floor (blue), a typical optical table setup in close proximity (orange), and the fidelity via a multitude of avenues from light field ampli- demonstrator setup with cooling fans turned off (green) and on tude fluctuation, lowering of the signal-to-noise ratio (red). through blurring or defocusing in the detection system, to light field dephasing noise [69–73]. We measure the vibrational stability of the setup using piezoelectric shear fans or modulations at the 50 Hz motor drive. Determin- accelerometers (Endevco 7703A-1000) at various loca- ing the origin of excess vibrations caused by the fans and tions in the setup. Time series data from the detectors is the structured noise at low frequencies is part of future recorded and Fourier transformed to voltage power spec- upgrade efforts, including dc-drive fans and improved air tral densities in an audio spectrum analyzer (Stanford flow direction. The performance is comparable to the Research Systems SR1). Voltage spectra are converted empty reference table in spite of the compact, towerlike to displacement spectral densities via the accelerome- construction in active operation, and validates engineering ter sensitivity calibration. The measurement is limited approaches used in the demonstrator. by the electronic noise floor of the signal conditioner (Endevco 133) below about 2 Hz. Displacement spectral C. Imaging and detection performance densities recorded simultaneously in the horizontal and Characterizing the performance of the primary imag- vertical directions are shown in Fig. 10, along with a refer- ing system provides information about the achievable ence spectrum obtained on an empty, broadband-damped, signal-to-noise ratio in readout, and the minimal achiev- honeycomb-lattice optical table in close proximity. Root- able spot size and crosstalk for addressing light. After mean-square displacements over the full measurement bandwidth are shown in Table I with the electronic back- ground subtracted. TABLE I. Root-mean-square (RMS) displacements over the The overall vibrational stability of the system is similar full measurement bandwidth for vibration measurements shown to traditional optical setups situated on dedicated optical in Fig. 10. Electronic background subtracted pointwise from tables. Spectra do show a clear influence of the operation spectra. of cooling fans used in the rack construction. The major- Optical Full w/o Full w/ ity of root-mean-square displacement is contributed at low Noise table fans fans frequencies below 10 Hz. Notably, these frequencies are RMShor. (nm) 54 21 61 275 also well below the fan rotation frequencies, indicating RMS (nm) 50 33 139 335 that they do not simply originate from vibrations of the vert.

020343-13 I. POGORELOV et al. PRX QUANTUM 2, 020343 (2021)

(a)

(b) Intensity (arb. units) (arb. Ion position (arb. units)

FIG. 11. Detection performance. (a) Fluorescence image of a linear string containing 11 ions. The axial trap frequency is ωax = 2π × 450 kHz, corresponding to a distance between the two center ions of 4 μm. (b) Integration over pixel columns shows well-separated ions. optimization of the objective alignment we resolve well- the micro-optics addressing unit and AOD addressing units separated ions in a 50-ion linear crystal. A typical image are presented. of an 11-ion crystal with minimal ion-ion separation of At this stage we utilize only four of the channels on the approximately 4 μm is shown in Fig. 11(a) recorded at micro-optics addressing unit. The beams from these chan- the detection wavelength of 397 nm. We determine the nels are fixed in position, and measuring the beam profile achieved imaging system magnification to be ×29.9 from proceeds by moving a single ion electrostatically along the known pixel dimensions and calculated ion spacings the trap axis through the beams by scanning the endcap for the used trap parameters. This is slightly larger than the voltages. At each position the light intensity is obtained design magnification of ×29. The high-NA readout optics by measuring the oscillation frequency of Rabi oscilla- enable camera detection times down to 300 μs at a fidelity tions. The Rabi frequency is proportional to the electric of about 99.9%. field at a given position. Figure 12(a) shows the esti- We determine the detection fidelity by preparing an ion mated light intensity along the trap axis obtained in this string either in the bright 4S1/2, or in the dark 3D3/2 mani- fashion. From a Gaussian fit to a higher-resolution scan fold by turning off the repumping laser at 866 nm. We elect shown in Fig. 12(b) we calculate a beam waist of w0 = to pursue this method over creation of the dark state via 0.81 ± 0.01 μm for all spots. Different coupling efficien- excitation using the 729 nm laser to avoid conflating oper- cies through FAOMs and waveguides lead to peak heights ational infidelities in qubit manipulation with detection varying across channels. infidelities. After a cooling period we perform a projective We further measure the resonant crosstalk between measurement and detect each ion individually on a camera. channels as defined by the ratio of the Rabi frequencies, From the counting statistics in each ion detection region we adjacent/addressed, when exciting a single ion. For the four determine the probability of measuring the prepared state active channels, we measure resonant crosstalk between for a given measurement time, that is, measure many (no) 1.9% and 3.4%, as shown in Fig. 12(c). This is much larger photons for the ion prepared in the bright (dark) state. We compared to what we would expect from a Gaussian beam estimate the detection crosstalk by determining the prob- with w0 = 0.81 μm or Airy fringes arising from the finite ability of measuring a bright state in a detection region aperture, and implies that the crosstalk is limited by optical in between two bright ions spaced at 5.9 μm. Detecting aberrations. light above the background in this empty region of space For the AOD addressing unit, we scan the addressing comes solely from detection crosstalk. At a measurement beam over a string of ions by changing the AOD drive fre- time of 300 μs we detect no events above the background quency. In this measurement we use laser pulses of a fixed threshold out of 10 000. Consequently, we conclude that power and duration such as to produce a pulse area of less detection crosstalk during our measurement windows is than π at the center of the beam. Scanning the beam across negligible. an ion will thus produce Rabi oscillations with maximal population in the excited state coinciding with maximal intensity. We calibrate the deflection per drive frequency increment obtained from the AODs by comparing the pop- D. Single-ion addressing performance ulation profile to the known ion distances at a given axial Addressing capabilities are crucial for the quantum com- center-of-mass mode frequency. The calibration yields a puting scheme we pursue. This capability is routinely deflection slope of 4.9 ± 0.1 μm/MHz. quantified in terms of the ability to resolve individual A measurement for a 16-ion string with a minimal ion sites along with the crosstalk between individual chan- distance of approximately 3.4 μm and a total length of nels. In the following, characterization measurements of approximately 60 μm is shown in Fig. 13(a). The intensity

020343-14 COMPACT ION-TRAP QUANTUM... PRX QUANTUM 2, 020343 (2021)

(a) Intensity (arb. units) Intensity (arb.

(c) (b) Intensity (arb. units) Intensity (arb.

FIG. 12. Micro-optics addressing unit performance. (a) A single ion’s position is scanned electrostatically along the trap axis by varying the endcap voltages. The square of the Rabi frequency is plotted as a function of this position for four active channels at a distance of 3.4 μm. Solid lines are Gaussian fits to data, alternating colours for clarity. (b) Same as (a) with higher resolution for spot size measurement of the focused addressing beam at 729 nm. By fitting a Gaussian distribution to the data we obtain a beam width of w0 ≈ 0.8 μm. Dashed black lines indicate the nearest neighbors for a 50-ion crystal at the minimal distance of approximately 3.2 μm. (c) Estimates of resonant crosstalk from intensity profiles in (a). The dashed entries in (c) are not assessed. profile shown in Fig. 13(b) is measured analogously to that E. Coherence properties and magnetic fields of the micro-optics addressing unit, yielding a beam waist Qubit coherence times are affected by a multitude of ≈ ± μ of w0 1.09 0.02 m. Next, we characterize the res- sources. Two common technical sources of decoherence onant and off-resonant crosstalk in a ten-ion string with in state-of-the-art trapped-ion setups are phase noise from μ a minimal inter-ion distance of 3.5 m. The ratio of the the driving fields and magnetic field noise. Phase noise Rabi frequencies of the nonaddressed ions to the addressed may originate either directly from laser frequency insta- ion is plotted in Fig. 13(c). We obtain an average resonant bility, that is, finite linewidth, or can be imparted through, crosstalk of 0.2% with a maximum of 1% on ion 5 when e.g., fiber noise or optical path length noise. Magnetic field addressing ion 4. The average nearest-neighbor crosstalk noise modulating the energy splitting in the qubit manifold is 0.5%. This is significantly lower than in the micro- often originates from mains or its harmonics, switching optics addressing unit. The difference may at least partly power supplies, or ground loops. be attributed to the better overall optical quality of macro- Phase noise in the driving field is ultimately lim- scopic precision optics used in the AOD approach, rather ited by the linewidth of the stabilized laser. Vibrational than micro-optical prototype components. isolation, rigid construction principles, fixing of flexi- Figure 13(d) shows the results of off-resonant crosstalk ble (fiber optics) paths, and air current control in free measurements. For this measurement, we perform a res- space are implemented throughout the setup to prevent onant collective π/2 pulse, followed by an addressed adding excess phase noise. Additionally, fiber noise can- ac-Stark pulse of variable length, followed by a collective celation is used up to the double-pass switching AOM; see −π/2 pulse. These composite pulses, sometimes referred Sec. III B 2. to as U(3) pulses, are used to reduce the effect of crosstalk. The influence of magnetic field noise depends on two The ac-Stark shift is proportional to the light field inten- factors: the noise present and the sensitivity of the utilized 2 sity I ∝ E while the√ Rabi frequency is proportional to transition to it. The qubit transition |4S1/2, mJ =−1/2↔ the electric field  ∝ I ∝ E. Consequently, we expect |3D5/2, mJ =−1/2 is the least sensitive to magnetic field the U(3) pulses to produce significantly smaller crosstalk. fluctuations out of the S1/2 ↔ D5/2 manifold, with a slope The maximum crosstalk measured is 2.6 × 10−4, 20 times of 5.6 MHz/mT. This is orders of magnitude higher than lower compared to the resonant crosstalk. The average in clock transitions of hyperfine qubits [74], and therefore crosstalk on nearest neighbors is 1.3 × 10−4. magnetic field stability as well as homogeneity have to be

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(a)

(b) (c) (d) Intensity (arb. units) Intensity (arb.

FIG. 13. AOD addressing unit performance. (a) Scan of the addressing beam over a 16-ion crystal. The population Pe is used as a proxy for the signal intensity; see the main text. Solid lines are Gaussian fits to data, alternating colours for clarity. (b) Spot size measurement of the focused addressing beam at 729 nm. A single ion’s position is scanned electrostatically along the trap axis by varying the endcap voltages. The square of the Rabi frequency is plotted as a function of this position. By fitting a Gaussian distribution to the data we obtain a beam width of w0 ≈ 1.1 μm. Dashed black lines indicate the nearest neighbors for a 50-ion crystal at the minimal distance of approximately 3.2 μm. (c) Resonant crosstalk measurements in a ten-ion crystal with minimal inter-ion distance of 3.5 μm. Plotted are the ratios of Rabi frequencies of ions relative to the addressed ion (white on the diagonal). (d) Same as (c) but using off-resonant, compensating U(3) pulses; see the main text. Ions where Rabi oscillations are too slow to fit reliably are set to 0 in the plot to avoid a spurious structure. precisely controlled in order to reach sufficient coherence Furthermore, we measure no influence of the vibration times of the order of T2 ≈ 100 ms or better. isolation elements on the coherence time of our qubit. The We characterize the temporal magnetic field stability by initial decay of fringe contrast is consistent with coherence opt = ± performing Ramsey spectroscopy on the ground state qubit times in excess of the T2 90 30 ms. However, for |4S1/2, mJ =−1/2↔|4S1/2, mJ =+1/2 transition in a waiting times longer than 25 ms, we observe accelerated single ion. This transition has a 5 times increased sen- contrast decay that limits the coherence time to the value sitivity to the magnetic field with respect to the qubit above, and causes substantial uncertainty. The source of transition, with a gradient of 28.0 MHz/mT. The opti- this enhanced decay is the subject of ongoing investigation, cal pulse sequence to access this transition begins with but may be caused by magnetic field noise induced by a π/2 pulse, which creates an equal superposition state switching magnets in neighboring experiments, or mains between |0 and |1.Aπ pulse then coherently trans- noise. This is further supported by two observations. First, fers the population from the optical qubit |0 state to the neighboring ion trap experiments implementing feedfor- |4S1/2, mJ =+1/2 state. After the Ramsey waiting time ward to cancel mains noise see a substantial improvement the sequence is reversed, which implements the Ramsey in coherence times. Second, a similar experiment being time evolution of an effective magnetic dipole transition. set up in a neighboring building with overall worse envi- This sequence yields a significant decrease in sensitiv- ronmental control but almost no other occupants causing ity to optical noise sources, thus isolating the influence magnetic field noise also shows increased coherence times. of the magnetic field. Performing Ramsey spectroscopy In addition, the spatial homogeneity of the magnetic with a closed μ-metal shield on the ground state qubit and field needs to be investigated to maintain coherence across GS = optical qubit yields respective coherence times of T2 an extended ion register. Small deviations in the position- ± opt = ± ing of the employed Halbach and Helmholtz configurations 18 1msandT2 90 30 ms, as shown in Figs. 14(b) and 14(c). This is sufficient to execute about 400 two- may cause a gradient or curvature across the trap axis. qubit gates or 4000 single-qubit gates during the coherence Likewise, the permanent magnet of the ion getter pump time. may cause a magnetic field gradient across the ion string.

020343-16 COMPACT ION-TRAP QUANTUM... PRX QUANTUM 2, 020343 (2021)

(a) (b)

(c)

FIG. 14. (a) Magnetic field gradient before compensation (blue, 3.2 ± 0.1 Hz/μm) and after compensation (red, 0.2 ± 0.1 Hz/μm) on the ground state qubit as seen from the Ramsey fringe frequency ωR for a fixed detuning as a function of ion position, corrected for linear frequency drift at fixed position. (b) Decay of Ramsey fringes of the dark state population P(D) for the ground state qubit over GS = ± time, resulting in a coherence time of T2 18 1 ms. (c) Same for the optical qubit transition. The sensitivity to magnetic fields is opt = ± 5 times lower, leading to less impact from magnetic field noise. We determine T2 90 30 ms.

We measure a gradient ∂zB = 0.111 ± 0.002 mT/mby and ωax = 2π × 1.05 MHz, we obtain a power-law depen- /ωα α ≈ performing Ramsey spectroscopy on the ground state qubit dency 1 ax with 1.7; see Fig. 15(b). and then shifting the equilibrium position of a single ion electrostatically. The gradient leads to a frequency shift on the ground state qubit transition of 3.1 ± 0.1 Hz/μm. G. Single-qubit gates Applying appropriate currents to the compensation coils Arbitrary single-qubit rotations are part of the complete reduces this axial gradient by an order of magnitude to gate set we chose to implement for universal quantum 0.2 ± 0.1 Hz/μm. For the 5 times less sensitive opti- computation capabilities. Qubit rotations are implemented cal qubit transition, this means a gradient of 0.041 ± differently depending on the sets of qubits required, and on 0.021 Hz/μm, corresponding to an end-to-end frequency the axis of rotation chosen. For many applications, rotating difference of approximately 8 Hz in a 200 μm chain of 50 all qubits collectively is required. This can be efficiently ions, as shown in Fig. 14(a). implemented using a single, collective beam traveling axi- ally along the spine of the trap, colinearly with the ion string. The single-site-resolving addressing units described F. Ion temperature and motional heating rates in Sec. IV D are used instead if only subsets of qubits need High-fidelity gate operations typically require the ions to be rotated. to retain coherence in their motional degrees of free- dom [16,75–77]. Motional coherence is ultimately limited (a) (b) by the motional heating rate. We therefore measure the ) ion temperature, that is, phononic mode occupation, and –1 from that, the heating rates with sideband thermometry (s [78]. Sideband thermometry can be applied for an aver- age phonon occupation n¯  2. Comparison of the Rabi oscillations on the red and blue sidebands of the qubit tran- sition yields the average phonon occupation [48]. After sideband cooling a single ion, we obtain a phonon number of n¯ph, ax = 0.02 ± 0.01 (at ωax = 2π × 1.05 MHz) in the axial direction, and n¯ph, rad = 0.06 ± 0.02 (at ωrad = 2π × 2.5 MHz) in the radial direction. By increasing the time between sideband cooling and temperature measurement we obtain a heating rate of 0.221 ± 0.007 s−1 in the axial − FIG. 15. Axial heating rates. (a) We calculate the heating rate ± 1 −1 direction [see Fig. 15(a)] and 0.3 0.1 s in the radial of n¯/tw = 0.221 ± 0.007 s at ωax = 1.05 MHz by fitting direction. These heating rates compare favorably with val- the increase in n¯ over the waiting time tw,wheren¯ is determined ues obtained in other traps operated at room temperature from sideband thermometry. (b) Heating rates are determined as [79] (see, in particular, Fig. 8). Measuring heating rates in (a) as a function of the trap frequency. The dashed line is a power-law fit 1/ωα ,whereα ≈ 1.7. for axial trap frequencies between ωax = 2π × 0.15 MHz ax

020343-17 I. POGORELOV et al. PRX QUANTUM 2, 020343 (2021)

The mechanism to drive the rotation itself is addition- (a) ally different depending on the axis chosen. A rotation around an axis in the Bloch sphere’s equatorial plane, ˆ ˆ that is, between Rx and Ry , can be implemented via res- onant excitation on the 729 nm qubit transition. An optical phase imparted using the FAOMs is used to define the axis of rotation relative to the first pulse in a sequence, ˆ which may be defined arbitrarily. The remaining axis, Rz, (b) is instead driven by off-resonant ac-Stark pulses. Typically, we perform π/2 rotations in 15 μs, limited by our current control electronics. In order to characterize the fidelity of these single qubit rotations we perform randomized benchmarking on a sin- gle qubit [80], assuming uncorrelated noise. A number of n Clifford gates is executed, where each Clifford gate incurs an average cost of 1.875 Rˆ (π). At the end of the sequence FIG. 16. (a) Parity oscillations after a Mølmer-Sørensen gate x on two ions followed by an evaluation pulse with phase .The the Clifford gate that inverts the sequence is added, thus amplitude of the parity oscillations is C2 = 0.995 ± 0.011 with creating an identity operation if not for gate errors. Here, 100 measurements per data point. Together with populations we concatenate up to 100 Clifford gates and fit an expo- P2(SS, DD) = 0.9988 ± 0.0005 we determine a fidelity of F2 = nential decay of the form A × pn + 0.5 to the population of 0.997 ± 0.006. (b) Parity oscillations of a 24-ion GHZ state with the initial state. We assume that the population will decay 100 measurements per data point. The parity contrast drops to to a value of 0.5 for a large number of gates. Then A + 0.5 C24 = 0.501 ± 0.013, the population to P24(S ···S, D ···D) = ± = ± is the fidelity of state initialization. The error per Clifford 0.588 0.006. We obtain a fidelity of F24 0.544 0.007; more than 6 standard deviations above the 24-partite entangle- gate is calculated as RClif = (1 − p)(1 − 1/d), with d = 2 denoting the dimension of the Hilbert space for a single ment threshold of 0.5. Measurement uncertainties are smaller than the marker size. qubit. First we characterize qubit rotations when using the global, axially-aligned beam that drives collective rota- tions. We obtain a Clifford gate fidelity of FClif = and providing a particularly easy-to-measure entanglement 99.83% ± 0.01% or Fgate = 99.91% ± 0.01% per single- witness. Furthermore, GHZ states are highly susceptible qubit rotation. We perform the same measurement on a to errors and decoherence [89–91], and as such, provide a single ion with the tightly focused beam from the micro- sensitive probe for characterizing the performance of our optics addressing unit, and obtain FClif = 99.75% ± 0.02% compound system. and Fgate = 99.86% ± 0.01%, respectively. First, we implement Mølmer-Sørensen gates using a col- lective, axially oriented beam on ion strings from 2 to 24 ions. The state fidelity F after the entangling oper- H. Mølmer-Sørensen gate and entanglement ation provides the entanglement witness with F > 0.5, generation guaranteeing full-depth entanglement. We characterize The ability to generate entanglement in a determinis- the operation using a two-ion crystal. The fidelity is tic way is key for quantum computation [81–83], and directly inferable from the populations in the |S, S=|1, 1 the missing component to our complete gate set. Differ- and |D, D=|0, 0 states with P2(SS, DD) = 0.9988 ± ent types of entangling gates have been proposed and 0.0005, as shown in Fig. 16(a), as well as their coher- demonstrated for trapped-ion qubits [49,84,85]. Here, we ences [89]. The coherences are obtained from observ- utilize the Mølmer-Sørensen gate [47,50] that generates ing the oscillations in the state’s parity as the phase of entanglement through spin-dependent forces generated by an analysis π/2 pulse is varied before projective mea- a bichromatic light field slightly detuned from a vibra- surement. Measuring the amplitude of this oscillation tional mode. However, quantifying the degree and depth yields C2 = 0.995 ± 0.011 [89,92]. From those we cal- of entanglement in many-body quantum systems gen- culate a single-gate state fidelity F2 = (P2 + C2)/2 with erated by any means remains a challenging task [86]. F = 0.997 ± 0.006. This fidelity includes all errors from Entanglement witnesses [87,88] are often used, where the state preparation and measurement (SPAM) and in partic- observable crossing a given threshold guarantees multipar- ular is achieved without postselection. A single two-ion tite entanglement of a given depth. Greenberger-Horne- Mølmer-Sørensen gate typically takes 200 μs. Sustaining Zeilinger (GHZ) states are a class of maximally entangled the interaction for odd-integer multiples of this duration Schrödinger’s cat states that have the fortunate features of implements repeated Mølmer-Sørensen gates. Measuring being natively implemented by the Mølmer-Sørensen gate, the fidelity after different numbers of gates, and fitting an

020343-18 COMPACT ION-TRAP QUANTUM... PRX QUANTUM 2, 020343 (2021)

(a)

(b)

FIG. 18. Full register overlap fidelity of states produced using the AOD addressing unit in a four-ion crystal. There is no mean- ingful distinction between pair (1,4) and (4,1) as opposed to in single-site addressing. Consequently, the matrix is symmetric.

leads to the question of the fidelity metric, with two promi- FIG. 17. Mølmer-Sørensen gate performance. (a) Decay of nent candidates. The first is the fidelity of, say, GHZ state overall state fidelity after repeated, odd-integer application of production where the nonaddressed subregister is ignored. μ approximately 200 s Mølmer-Sørensen interactions for axial This will quantify the action of an entangling gate, but and radial two-ion gates. We infer a single-gate state fidelity of is oblivious to what this operation does to the rest of the 0.9983 ± 0.0001 per axial gate and 0.9936 ± 0.0003 per radial gate. (b) Axial Mølmer-Sørensen gates on a linear ion string for register. The second, more stringent choice, would be to different ion numbers. Pairs of ions are successively added to the determine the fidelity of performing an entangling oper- existing string and the measurement repeated. Blue circles rep- ation on the addressed qubits without affecting the idling resent measurements performed at an axial center-of-mass mode qubits. This is then the overlap of the full register state frequency of ωax = 2π × 234 kHz, to ensure the formation of a with the ideal register state, rather than subregisters. Given linear string for a large number of ions, and are taken consec- that crosstalk is unavoidable we elect to chose the second utively. Blue triangles represent measurements performed at an metric. ω = π × axial center-of-mass mode frequency of ax 2 200 to 1000 Initial tests are carried out with the micro-optics address- kHz on different days. Measurement uncertainties are smaller ing unit, addressing the two outer ions of a three-ion than the marker size. crystal. The Mølmer-Sørensen gate with the radially ori- ented addressing beam yielded a register overlap fidelity of exponential decay as shown in Fig. 17(a) yields a sim- F2 = 0.989 ± 0.005 for a single gate. Again, concatenat- ple estimator of the state fidelity with 0.9983 ± 0.0001 per ing multiple gates and fitting an exponential decay yields gate. = ± a fidelity of F2 0.9936 0.0003 per gate as plotted in Larger multipartite entangled states are subsequently Fig. 17(a). Here F2 is the fidelity of the Mølmer-Sørensen produced by applying a single Mølmer-Sørensen gate to gate including SPAM errors, while F2 is approximately the multiple ions. We demonstrate the generation of GHZ pure fidelity per gate operation without SPAM errors. states up to 24 qubits. Measured fidelities are plotted in With the AOD addressing unit we measure all pairwise- Fig. 17(b), where pairs of ions are successively added to entangling gates in a four-ion crystal. We calibrate the gate the existing string and the measurement is repeated. For 24 on the two outer ions and use the same set of parameters ( ··· ··· ) = ± ions, we measure P24 S S, D D 0.588 0.006, for all gates. The register overlap fidelities are shown in = ± = ± C24 0.501 0.013, and F24 0.544 0.007, which is Fig. 18. We achieve fidelities in the range from 0.969(7) again not corrected for SPAM errors and without post- to 0.986(8). Cumulative population in the nominally non- selection, and is more than 6 standard deviations above addressed subregister for these measurements is below the threshold for 24-partite entanglement [89]. The parity 0.2%. oscillations are plotted in Fig. 16(b). To the best of our We anticipate that further improvements in the radial knowledge, this is the largest GHZ state as well as the mode stability, cooling of radial modes, addressing unit largest fully entangled state that has been generated in any and mode disentanglement [93–95] should increase the system without error mitigation or postselection. fidelity of the addressed gates. In the data shown above Mølmer-Sørensen gates were carried out on the axial modes of vibration. In order to cre- V. CONCLUSION ate a fully programmable system, we use the radial modes of vibration for arbitrary-pair, addressed entangling opera- In this manuscript we have provided a detailed descrip- tions on specific qubits in long ion strings. Characterizing tion of the experimental implementation of a compact, the creation of states with addressed operations naturally trapped-ion quantum computing demonstrator situated in

020343-19 I. POGORELOV et al. PRX QUANTUM 2, 020343 (2021) two 19-inch racks. We have presented mechanical, optical, (a) and electrical systems along with characterizing experi- ments. This experimental platform improves upon conven- (b) tional hardware implementations in terms of modularity, integration, and remote control. In our characterization measurements we find the system performance to be on par FIG. 19. Ion images of (a) 24 and (b) 50 ions in the demon- with conventional, laboratory-based hardware implemen- strator. The 24-ion chain is used to demonstrate 24-partite entan- tations in terms of experimentally relevant performance glement within the setup without the use of postselection or error criteria. We find that mechanical stability, optical read- mitigation. Fifty-ion chains are the midterm control target and out and addressing performance, heating rates, coherence can already be trapped and cooled. Nonuniform brightness stems times, and Mølmer-Sørensen entangling fidelities in the from the finite size of the detection beam. current implementation do not suffer relative to tradi- tional optical table setups. Using the compound system, power loss for multisite addressing, and off-axis spots limit we are able to produce maximally entangled Greenberger- this technology to the simultaneous addressing of a small Horne-Zeilinger states with up to 24 qubits with a fidelity number of ions. of 54.4% ± 0.7%. To our knowledge, this is the largest With both of these approaches we demonstrate single- maximally entangled state yet generated in any system qubit and pairwise-entangling gates on registers up to without the use of error mitigation or postselection, and 10 ions. From randomized benchmarking we obtain a demonstrates the capabilities of our system. fidelity of Fgate = 99.86% ± 0.01% per addressed single- In addition, we presented site-selective qubit operations ion gate. Measurements of resonant crosstalk are shown to implement a complete gate set for universal quantum to be below 1% across the entire ten-ion register with the computation using two distinct approaches to addressing: a AOD approach, while nonresonant crosstalk is measured to micro-optics approach with fixed, rigid waveguides, and an be less than 1.25 × 10−4 in the same string. Together with acousto-optic deflector approach. Both of these approaches the pairwise-entangling operations with fidelities between offer advantages over the other in particular settings. 97% and 99% we show all the basic operations for a fully The micro-optics approach readily offers itself for simul- programmable quantum system. Benchmarking of larger taneous multisite addressing without producing off-axis registers, and with more complete suites of benchmarking spots that can lead to resonant and off-resonant crosstalk. tools [96] will be undertaken as part of the next round of The power scaling in such a scenario is linear in the hardware integration and software improvements. number of channels, assuming a suitable power distribu- These near- and midterm upgrades to the hardware and tion system is at hand. Parallel radial sideband cooling software stacks will further improve upon the demonstra- is one direct beneficiary of such capabilities, as is direct tor’s capabilities. Use of an external master oscillator to generation of interaction between more than two qubits. generate the narrow-linewidth qubit laser will no longer Individual control over amplitude, phase, and frequency of be required after installation of the compact diode-laser each channel is a fundamental advantage of this approach source that is currently under construction as part of the but requires one FAOM per qubit. The positional stability AQTION collaboration. Similarly, single-site addressing is not affected by the oscillator stability of rf sources, and capabilities will be improved in mode quality and the num- extension to larger registers are not limited by the speed of ber of channels. This will allow the setup to implement sound or similar quantities such as in AOD-based devices. more complex algorithms by moving from axial gates to The AOD approach on the other hand is technologi- radial quantum gates enhanced by established quantum cally simpler, thus offering superior performance at this control techniques [97,98]. Upgrades to M-ACTION, as stage. Optical quality of macroscopic components is often well as complimentary developments to the control and also superior to micro-optics, in particular in prototyp- remote access software stack will enable easier access ing scenarios such as here, which reduces abberations. to the demonstrator capabilities in a hardware-agnostic The addressing is inherently flexible, such that it can be fashion. adjusted for qubit registers from 2 ions to 40 ions in our Already, the device presented is capable of operating configuration. Adjustment of power and optical phase of with qubit numbers on par with state-of-the-art conven- individual channels is possible without an optical modula- tional laboratory setups. An image of such a qubit register tor per ion, which significantly reduces the technological is shown in Fig. 19(a). The midterm upgrades should overhead compared to the micro-optics approach. This enable us to increase this number to the AQTION control unit is fed by a single fiber, and no prior power dis- target of 50 qubits and beyond. We have already demon- tribution capabilities are required. The switching speed strated basic capabilities of control in larger qubit chains in AODs is limited ultimately by the speed of sound as shown in Fig. 19(b), with a 50-ion chain already crys- in the deflecting crystal, which therefore also limits the tallized in our trap. In the long term, we hope that the speed at which operations can be performed. The quadratic demonstrator’s features and engineering solutions mean

020343-20 COMPACT ION-TRAP QUANTUM... PRX QUANTUM 2, 020343 (2021) that ion-trap-based quantum computers may be situated [10] X. L. Wang et al., 18-Qubit Entanglement with Six Pho- in any space with reasonable environmental stability and tons’ Three Degrees of Freedom, Phys. Rev. Lett. 120, vibrational level. Quantum computation with a qubit count 260502 (2018). exceeding 100 is feasible based on our architecture and this [11] C. H. Yang et al., Operation of a silicon quantum processor characterization of its first implementation. unit cell above one kelvin, Nature 580, 350 (2020). [12]J.J.Pla,K.Y.Tan,J.P.Dehollain,W.H.Lim,J.J.L. Morton, D. N. Jamieson, A. S. Dzurak, and A. Morello, A single-atom electron spin qubit in silicon, Nature 489, 541 (2012). ACKNOWLEDGMENTS [13] P. Shor, in 37th Annual Symposium on Foundations of Computer Science (FOCS ’96) (IEEE, 1996), Vol. 00, We gratefully acknowledge funding from the EU p. 56. H2020-FETFLAG-2018-03 under Grant Agreement No. [14] J. Benhelm, G. Kirchmair, C. F. Roos, and R. Blatt, 820495. We also acknowledge support by the Austrian Towards fault-tolerant quantum computing with trapped Science Fund (FWF), through the SFB BeyondC (FWF ions, Nat. Phys. 4, 463 (2008). Project No. F7109), and the IQI GmbH. This project [15] D. Nigg, M. Müller, E. A. Martinez, P. Schindler, M. Hen- has received funding from the European Union’s Hori- nrich, T. Monz, M. A. Marting-Delgado, and R. Blatt, zon 2020 research and innovation programme under the Quantum computations on a topologically encoded qubit, Marie Skłodowska-Curie Grant Agreement No. 840450. Science 345, 302 (2014). P.S. and M.M. acknowledge support from the Austrian [16] C. J. Ballance, T. P. Harty, N. M. Linke, M. A. Sepiol, and D. M. Lucas, High-Fidelity Quantum Logic Gates Research Promotion Agency (FFG) contract 872766. P.S., Using Trapped-Ion Hyperfine Qubits, Phys. Rev. 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